Parametric resonances for torsional vibration of excited rotating machineries with nonconstant velocity joints

Abstract

The shaft system is a rotating machinery with many applications due to its high speed. The angle between shafts may not be zero. So the shafts can be connected to each other through a nonconstant velocity U-joint, which transforms a constant input angular velocity into a periodically fluctuating velocity. Consequently, the mechanism is parametrically excited and may face resonance conditions. Herein, a power transmission system including three elastic shafts is considered. The polar inertia moment of each shaft is modeled as a dynamic system with two discrete disks at the shaft ends. The equations of motion consist of a set of Mathieu–Hill differential equations with periodic coefficients. The dynamic stability and torsional vibration of the shaft system are analyzed. The system geometry and inertia moment effect are the main issues in this contribution. Parametric instability charts are achieved via the monodromy matrix technique. The graphical numerical results are validated with the frequency analytical results. Finally, the stability regions are shown in the parameter spaces of velocity, misalignment angles and the inertia of disks. The results demonstrated that by changing the system inertia and geometry, stabilizing the whole system is possible. Moreover, to check the precision of the model, the results are compared with a basic single-disk model, which is prevalent in two-shaft systems.

A Comprehensive Study of Cardon Shaft Using Modal Analysis

“…Figure 1: Cardon Shaft The primary focus in the early years [7,8] was on the parametric instability in a multibody shaft system stimulated by universal joints for various complex rotor-bearing systems. The aforementioned investigation was focused and efficient for a linear system.…”

Nonlinear stability analysis of piecewise actuated piezoelectric microstructures

“…Such systems are being appeared in an extensive variety of applications, including sensors/actuators, capacitive switches, smart systems, tunable valves, ultra-sensitive detectors, and biodevices [1][2][3][4][5][6][7]. Analyzing the structural behavior and instability conditions of these systems are essential to improve their design and performance [8][9][10][11][12][13][14][15].…”

Effective damping of the torsional vibrations of the drive system with an elastic joint based on the forced dynamic control algorithms

“…The torsional vibrations have been originally recognized in big industrial drives, such as rolling mill drives, lifting and conveyer drives and others (Hori et al., 1999; Zhang and Tong, 2006; Valenzuela et al., 2009). Nowadays they have become evident in modern high-performance drives, such as servo drives, robot arm drives or wind mill turbines (Montague et al., 2013; Bartschat et al., 2016; Wang et al., 2016; Yang et al, 2016; SoltanRezaee et al., 2018).…”